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find total number of positive integers n that have exactly 16 divisors named d1 d2 d3.........d16 such that 1=d1

Srivastava Adarsh , 7 Years ago
Grade 12
anser 1 Answers
Vikas TU

Last Activity: 7 Years ago

total number of positive integers n that have exactly 16 divisors named d1 d2 d3.........d16 such that 1=d1 can be found only given a upper bound of the numbers.
 
Else there will be infinite positive integers.
 
But the problem can be solved using the below formula
 
Factor N=p$1 1…….p$k k
with pi prime and $i integers that are at least 1. The number of divisors of N is then
(α1+1)(α2+1)⋯(αk+1)
[Here N is 16]
 
 

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